Diwa de Leon holding a frisbee: Carlos, a Spanish-speaking volunteer with Georgia Latino Alliance for Human Rights, and Adelina Nicholls, the group’s executive director, spoke with a day laborer in Atlanta earlier this month.

© Melissa Golden for The New York Times
Carlos, a Spanish-speaking volunteer with Georgia Latino Alliance for Human Rights, and Adelina Nicholls, the group’s executive director, spoke with a day laborer in Atlanta earlier this month.

More than 2,000 migrants who were in the United States illegally were targeted in widely publicized raids that unfolded across the country last week. But figures the government provided to The New York Times on Monday show that just 35 people were detained in the operation.

President Trump had touted the raids — called Operation Border Resolve — as a show of force amid an influx of Central American parents and children across the southern border. After postponing the raids in June, Mr. Trump said ahead of time that they would take place last week.

Two current Department of Homeland Security officials and one former department official also confirmed to The Times that an enforcement operation would take place around mid-July.

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But the publicity may have prompted many of those who had been targeted — 2,105 people in more than a dozen cities who had received final deportation orders but had not reported to Immigration and Customs Enforcement officers — to temporarily leave their homes, or to move altogether to evade arrest.

Advance notice of the large-scale operation also gave immigrant advocates time to counsel families about their rights, which include not opening the door or answering questions. On social media, community groups shared detailed information about sightings of ICE agents.

In an interview Monday, Matthew Albence, the acting director of ICE, which is responsible for arresting, detaining and deporting unauthorized immigrants who are already in the United States, acknowledged that the number of apprehensions was low.

“I don’t know of any other population where people are telling them how to avoid arrest as a result of illegal activity,” he said. “It certainly makes it harder for us to effectuate these orders issued.”

“You didn’t hear ICE talking about it before the operation was taking place,” he added.

The arrests of the nearly three dozen migrants — 17 of whom were members of families that crossed the border together and 18 of whom were so-called collateral apprehensions of undocumented people — were among more than 900 that the immigration authorities have made since mid-May, Mr. Albence said.

From May 13 through July 11, ICE arrested 899 adults who had final deportation orders, in an undertaking called Operation Cross Check. The majority had criminal convictions, Mr. Albence said.

[What happens after an ICE raid? Here’s an explaination of the deportation process.]

A backlog of nearly one million immigration cases means that it can take years for a case to wind its way through the courts. Those who were targeted in last week’s raids had been placed on an accelerated docket, with a goal of resolving their cases within a year. The majority had been ordered removed from the country by an immigration judge.

“What we found is that the vast majority did not even show up for their first hearing,” Mr. Albence said. “Above and beyond, we sent them letters giving them the opportunity to turn themselves in and arrange for an orderly removal process,” including time to organize their affairs and schedule flights on commercial carriers.

As part of a multipronged approach to rein in illegal immigration, Mr. Albence said that the government had also been cracking down on companies suspected of hiring undocumented immigrants. He said 3,282 businesses across the country were told last week to submit payroll documents for review.

“Part of our goal is to reduce economic opportunities,” Mr. Albence said. “We cannot have individuals who come into the country illegally and then go find work illegally.”

The audits of companies and payroll forms, often called “silent raids,” hit restaurants, food processing, high-tech manufacturing, agriculture and other industries that employ thousands of workers, according to lawyers representing some of the companies. Employers typically lose a substantial number of workers as a result of the audits, which can also lead to fines and criminal charges against the businesses.

The Trump administration has significantly increased company inspections, often called I-9 audits for the form that workers are required to fill out affirming that they are authorized to work in the United States. There were 5,981 such audits in fiscal 2018 compared to 1,360 the previous year.

“The Trump administration has been more aggressive than any administration with I-9 investigations,” said Kimberley Robidoux, a business immigration lawyer in San Diego who specializes in compliance and who has several clients who are affected.

Still, as it grapples with a record number of migrant families at the southern border, the Trump administration has so far deported fewer people, on average each year, than the Obama administration.

In fiscal year 2018, the Trump administration deported 256,086 immigrants, an increase of 13 percent over the previous year. In contrast, President Barack Obama removed 409,849 people in 2012, an all-time high, and 235,413 in fiscal year 2015.

In the first two quarters of the 2019 fiscal year, the Trump administration deported 130,432 people, up from 123,253 during the same period the previous year.

Mr. Obama directed immigration authorities to target for arrest and removal convicted criminals, migrants who had crossed the border recently and those who had illegally entered the country multiple times. Mr. Trump has said that anyone agents encounter who is living in the country illegally is fair game for detention and removal.

Indeed, on Monday the Trump administration said that it would accelerate the deportation of undocumented immigrants who cannot prove they have been in the United States for more than two years, enabling federal agents to arrest and deport people without a hearing before a judge.

The expansion of a so-called expedited removals program, which is expected to be challenged in court, could result in people being deported without a court hearing and could affect their ability to seek asylum in the United States.

Just last week, the administration announced it would deny protections to immigrants who failed to apply for asylum in at least one country they passed through on their way north, in its latest attempt to deter Central Americans from heading to the United States. That policy was challenged in court by a coalition of immigrant advocates one day after it was announced.

The Border Patrol has arrested 363,300 migrant family members from Honduras, El Salvador and Guatemala at the southern border so far in fiscal year 2019. Many of them are seeking asylum, having fled violence in their home countries.

Because children cannot be detained for more than 20 days under established standards, the Border Patrol has been releasing families, who usually turn themselves in to authorities after crossing the border, to await their immigration court dates.

“This highlights the challenges when we are unable to detain individuals at the border and are forced to release them into the country,” Mr. Albence said.

Last week, Mr. Trump deemed the operation targeting families that began around July 14 as “very successful.”

The government’s plans changed at the last minute because of news reports that had tipped off immigrants about what to expect, according to several current and former Department of Homeland Security officials. Instead of a large sweep, the authorities opted for a limited and more diffuse scale of apprehensions.

The families who were rounded up have been placed in family detention centers, where it is difficult for them to gain access to legal help. But immigration lawyers said that they could still take steps to halt their immediate deportation, for example by filing an appeal or a motion to reopen their cases. Some of the families, they said, might not have been aware they missed a court hearing if they did not receive a notice of if they had moved.

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